NDSolve:无法求得一个导数公式，考虑使用选项设置：......
大致看一下这是什么问题？我在知乎上问说没有见过。
这个代码有些长，我在评论区也补上了一部分。
l = 1
g = 2
w = 2
b = 2
a = 3
\[Theta] = 2
m = 1
L10 = 1/6 (-6 g w (l Cos[\[Theta]] Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] +
Sin[\[Theta]] (b + l Sin[\[Theta] - \[Beta]1[t]])) -
3 m (3 b Sin[\[Theta]] + a Cos[\[Theta]] Sin[\[Alpha]1[t]] -
2 l Cos[\[Beta]1[t]] Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2]) -
6 g w (Cos[\[Theta]] (-l Cos[\[Alpha]1[
t]] (-2 Cos[\[Theta] - \[Beta]1[t]] +
Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[t]]) +
2 a Sin[\[Alpha]1[t]]) +
Sin[\[Theta]] (b + 2 l Sin[\[Theta] - \[Beta]1[t]] -
l Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]])) + (
a^2 (a + 3 b) m Derivative[1][\[Alpha]1][t]^2)/(4 (a + b)) +
1/(4 (a^2 + 4 l^2 Cos[\[Theta] - \[Beta]1[t]]^2))
3 m ((a^2 + 2 l^2 + 2 l^2 Cos[2 \[Theta] - 2 \[Beta]1[t]]) Sin[
ArcTan[(2 l Cos[\[Theta] - \[Beta]1[t]])/a] + \[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] +
2 l (-l Cos[
ArcTan[(2 l Cos[\[Theta] - \[Beta]1[t]])/a] + \[Alpha]1[
t]] Sin[2 \[Theta] - 2 \[Beta]1[t]] +
a Sin[ArcTan[(2 l Cos[\[Theta] - \[Beta]1[t]])/
a] + \[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[
t]]) Derivative[1][\[Beta]1][t])^2 +
2 l^2 w (Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] -
Cos[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t] +
Cos[\[Theta] - \[Beta]1[t]]^2 Derivative[1][\[Beta]1][
t]^2 + (Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] Derivative[1][\[Alpha]1][
t] + Sin[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[1][\[Beta]1][
t])^2) +
3 m ((1/2 a Cos[\[Theta]] Cos[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] +
l Sqrt[Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2]
Sin[\[Beta]1[t]] Derivative[1][\[Beta]1][t] + (
l Cos[\[Theta] - \[Beta]1[t]] Cos[\[Beta]1[t]] Sin[\[Alpha]1[
t]] (Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t]))/Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2])^2 + (1/
2 a Cos[\[Alpha]1[t]] Sin[\[Theta]] Derivative[
1][\[Alpha]1][t] +
l Cos[\[Beta]1[t]] Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2]
Derivative[1][\[Beta]1][t] - (
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[t]] Sin[\[Beta]1[
t]] (Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t]))/Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2])^2) + (
2 ((l Cos[\[Alpha]1[t]] Cos[\[Theta] - \[Beta]1[t]] +
a Sin[\[Alpha]1[t]]) Derivative[1][\[Alpha]1][t] +
l Sin[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t])^3)/(
Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])) - (2 (Cos[\[Theta]] (a Cos[\[Alpha]1[t]] -
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]]) Derivative[1][\[Alpha]1][t] +
l (-Cos[\[Theta] - \[Beta]1[t]] Sin[\[Theta]] +
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t]]) Derivative[
1][\[Beta]1][t])^3)/(Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[
t] + \[Phi]1[t]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][
t] + (Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] -
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]]) (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])) + (2 (a Cos[\[Theta]] Cos[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] -
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] +
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Alpha]1[t]] Derivative[1][\[Alpha]1][t] -
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Theta]] Derivative[
1][\[Beta]1][t] +
l Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[1][\[Beta]1][
t] + l (Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] -
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]]) (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t]))^3)/(Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[
t] + \[Phi]1[t]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][
t] + (Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] -
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]]) (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])) + (2 (a Cos[\[Alpha]1[t]] Sin[\[Theta]] Derivative[
1][\[Alpha]1][t] +
l Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] +
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t] -
l Sin[\[Theta]] (Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] -
Cos[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t]) +
Cos[\[Theta] - \[Beta]1[t]] Cos[\[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) -
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) +
l Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[t]] Sin[\[Phi]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t])^2)^3)/(Cos[\[Theta] - \[Beta]1[
t] + \[Phi]1[t]] Sin[\[Theta]] Sin[\[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] -
Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) +
Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[t]] Sin[\[Phi]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])^2) - (2 (Sin[\[Theta]] (a Cos[\[Alpha]1[t]] -
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]]) Derivative[1][\[Alpha]1][
t] + (l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t]] +
Cos[\[Theta] - \[Beta]1[t]] Cos[\[Phi]1[t]] +
l Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[
t]]) Derivative[1][\[Beta]1][t] -
Cos[\[Theta] - \[Beta]1[t]] Cos[\[Phi]1[t]] Derivative[
1][\[Phi]1][t])^3)/(Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] -
Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) +
Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[t]] Sin[\[Phi]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])^2) - (2 ((a Sin[\[Alpha]1[t]] +
2 l Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]/
2] Sin[\[Phi]1[t]/2]) Derivative[1][\[Alpha]1][t] +
l Sin[\[Alpha]1[
t]] ((Sin[\[Theta] - \[Beta]1[t]] -
Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]]) Derivative[
1][\[Beta]1][t] +
Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] Derivative[
1][\[Phi]1][t]))^3)/(Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] - Derivative[1][\[Phi]1][t])))
LAGELANGRI1 =
D[L10, \[Alpha]1[t]] - Derivative[D[L10, \[Alpha]1'[t]], t]
LAGELANGRI2 = D[L10, \[Beta]1[t]] - Derivative[D[L10, \[Beta]1'[t]], t]
LAGELANGRI3 = D[L10, \[Phi]1[t]] - Derivative[D[L10, \[Phi]1'[t]], t]
NDSolve[{LAGELANGRI1 == 0, LAGELANGRI2 == 0,
LAGELANGRI3 ==
0, \[Phi]1[0] == \[Phi]0, \[Beta]1[0] == \[Beta]0, \[Alpha]1[
0] == \[Alpha]0, \[Alpha]1'[0] == q, \[Beta]1'[0] ==
p, \[Phi]1'[0] == s}, {\[Alpha]1[t], \[Beta]1[t], \[Phi]1[t]}, {t,
0.6, 0.61}]
(*DSolve[{LAGELANGRI1==0,LAGELANGRI2==0,LAGELANGRI3==0,\[Phi]1[0]==\
\[Phi]0,\[Beta]1[0]==\[Beta]0,\[Alpha]1[0]==\[Alpha]0,\[Alpha]1'[0]==\
q,\[Beta]1'[0]==p,\[Phi]1'[0]==s},{\[Alpha]1[t],\[Beta]1[t],\[Phi]1[t]\
},t] *)
大致看一下这是什么问题？我在知乎上问说没有见过。
这个代码有些长，我在评论区也补上了一部分。
l = 1
g = 2
w = 2
b = 2
a = 3
\[Theta] = 2
m = 1
L10 = 1/6 (-6 g w (l Cos[\[Theta]] Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] +
Sin[\[Theta]] (b + l Sin[\[Theta] - \[Beta]1[t]])) -
3 m (3 b Sin[\[Theta]] + a Cos[\[Theta]] Sin[\[Alpha]1[t]] -
2 l Cos[\[Beta]1[t]] Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2]) -
6 g w (Cos[\[Theta]] (-l Cos[\[Alpha]1[
t]] (-2 Cos[\[Theta] - \[Beta]1[t]] +
Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[t]]) +
2 a Sin[\[Alpha]1[t]]) +
Sin[\[Theta]] (b + 2 l Sin[\[Theta] - \[Beta]1[t]] -
l Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]])) + (
a^2 (a + 3 b) m Derivative[1][\[Alpha]1][t]^2)/(4 (a + b)) +
1/(4 (a^2 + 4 l^2 Cos[\[Theta] - \[Beta]1[t]]^2))
3 m ((a^2 + 2 l^2 + 2 l^2 Cos[2 \[Theta] - 2 \[Beta]1[t]]) Sin[
ArcTan[(2 l Cos[\[Theta] - \[Beta]1[t]])/a] + \[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] +
2 l (-l Cos[
ArcTan[(2 l Cos[\[Theta] - \[Beta]1[t]])/a] + \[Alpha]1[
t]] Sin[2 \[Theta] - 2 \[Beta]1[t]] +
a Sin[ArcTan[(2 l Cos[\[Theta] - \[Beta]1[t]])/
a] + \[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[
t]]) Derivative[1][\[Beta]1][t])^2 +
2 l^2 w (Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] -
Cos[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t] +
Cos[\[Theta] - \[Beta]1[t]]^2 Derivative[1][\[Beta]1][
t]^2 + (Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] Derivative[1][\[Alpha]1][
t] + Sin[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[1][\[Beta]1][
t])^2) +
3 m ((1/2 a Cos[\[Theta]] Cos[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] +
l Sqrt[Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2]
Sin[\[Beta]1[t]] Derivative[1][\[Beta]1][t] + (
l Cos[\[Theta] - \[Beta]1[t]] Cos[\[Beta]1[t]] Sin[\[Alpha]1[
t]] (Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t]))/Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2])^2 + (1/
2 a Cos[\[Alpha]1[t]] Sin[\[Theta]] Derivative[
1][\[Alpha]1][t] +
l Cos[\[Beta]1[t]] Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2]
Derivative[1][\[Beta]1][t] - (
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[t]] Sin[\[Beta]1[
t]] (Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t]))/Sqrt[
Cos[\[Alpha]1[t]]^2 Cos[\[Theta] - \[Beta]1[t]]^2 +
Sin[\[Theta] - \[Beta]1[t]]^2])^2) + (
2 ((l Cos[\[Alpha]1[t]] Cos[\[Theta] - \[Beta]1[t]] +
a Sin[\[Alpha]1[t]]) Derivative[1][\[Alpha]1][t] +
l Sin[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t])^3)/(
Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])) - (2 (Cos[\[Theta]] (a Cos[\[Alpha]1[t]] -
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]]) Derivative[1][\[Alpha]1][t] +
l (-Cos[\[Theta] - \[Beta]1[t]] Sin[\[Theta]] +
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t]]) Derivative[
1][\[Beta]1][t])^3)/(Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[
t] + \[Phi]1[t]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][
t] + (Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] -
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]]) (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])) + (2 (a Cos[\[Theta]] Cos[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] -
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] +
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Alpha]1[t]] Derivative[1][\[Alpha]1][t] -
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Theta]] Derivative[
1][\[Beta]1][t] +
l Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[1][\[Beta]1][
t] + l (Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] -
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]]) (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t]))^3)/(Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[
t] + \[Phi]1[t]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][
t] + (Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] -
Cos[\[Theta]] Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]]) (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])) + (2 (a Cos[\[Alpha]1[t]] Sin[\[Theta]] Derivative[
1][\[Alpha]1][t] +
l Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] +
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t] -
l Sin[\[Theta]] (Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] -
Cos[\[Alpha]1[t]] Sin[\[Theta] - \[Beta]1[t]] Derivative[
1][\[Beta]1][t]) +
Cos[\[Theta] - \[Beta]1[t]] Cos[\[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) -
l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) +
l Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[t]] Sin[\[Phi]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t])^2)^3)/(Cos[\[Theta] - \[Beta]1[
t] + \[Phi]1[t]] Sin[\[Theta]] Sin[\[Alpha]1[
t]] Derivative[1][\[Alpha]1][t] -
Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) +
Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[t]] Sin[\[Phi]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])^2) - (2 (Sin[\[Theta]] (a Cos[\[Alpha]1[t]] -
l Cos[\[Theta] - \[Beta]1[t]] Sin[\[Alpha]1[
t]]) Derivative[1][\[Alpha]1][
t] + (l Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t]] +
Cos[\[Theta] - \[Beta]1[t]] Cos[\[Phi]1[t]] +
l Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[
t]]) Derivative[1][\[Beta]1][t] -
Cos[\[Theta] - \[Beta]1[t]] Cos[\[Phi]1[t]] Derivative[
1][\[Phi]1][t])^3)/(Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] Sin[\[Theta]] Sin[\[Alpha]1[t]] Derivative[
1][\[Alpha]1][t] -
Cos[\[Theta]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[
t]] (Derivative[1][\[Beta]1][t] -
Derivative[1][\[Phi]1][t]) +
Cos[\[Alpha]1[
t]] Sin[\[Theta]] Sin[\[Theta] - \[Beta]1[t]] Sin[\[Phi]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] -
Derivative[1][\[Phi]1][
t])^2) - (2 ((a Sin[\[Alpha]1[t]] +
2 l Cos[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]/
2] Sin[\[Phi]1[t]/2]) Derivative[1][\[Alpha]1][t] +
l Sin[\[Alpha]1[
t]] ((Sin[\[Theta] - \[Beta]1[t]] -
Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]]) Derivative[
1][\[Beta]1][t] +
Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] Derivative[
1][\[Phi]1][t]))^3)/(Cos[\[Alpha]1[
t]] Cos[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] Derivative[
1][\[Alpha]1][t] +
Sin[\[Alpha]1[
t]] Sin[\[Theta] - \[Beta]1[t] + \[Phi]1[t]] (Derivative[
1][\[Beta]1][t] - Derivative[1][\[Phi]1][t])))
LAGELANGRI1 =
D[L10, \[Alpha]1[t]] - Derivative[D[L10, \[Alpha]1'[t]], t]
LAGELANGRI2 = D[L10, \[Beta]1[t]] - Derivative[D[L10, \[Beta]1'[t]], t]
LAGELANGRI3 = D[L10, \[Phi]1[t]] - Derivative[D[L10, \[Phi]1'[t]], t]
NDSolve[{LAGELANGRI1 == 0, LAGELANGRI2 == 0,
LAGELANGRI3 ==
0, \[Phi]1[0] == \[Phi]0, \[Beta]1[0] == \[Beta]0, \[Alpha]1[
0] == \[Alpha]0, \[Alpha]1'[0] == q, \[Beta]1'[0] ==
p, \[Phi]1'[0] == s}, {\[Alpha]1[t], \[Beta]1[t], \[Phi]1[t]}, {t,
0.6, 0.61}]
(*DSolve[{LAGELANGRI1==0,LAGELANGRI2==0,LAGELANGRI3==0,\[Phi]1[0]==\
\[Phi]0,\[Beta]1[0]==\[Beta]0,\[Alpha]1[0]==\[Alpha]0,\[Alpha]1'[0]==\
q,\[Beta]1'[0]==p,\[Phi]1'[0]==s},{\[Alpha]1[t],\[Beta]1[t],\[Phi]1[t]\
},t] *)
